# Tagged Questions

In QFT, regularization is a method of addressing divergent expressions by introducing an arbitrary regulator, such as a minimal distance *ϵ* in space, or maximal energy *Λ*. While the physical divergent result is obtained in the limit in which the regulator goes away, *ϵ* → 0 or *Λ* → ∞, the ...

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### Why does analytic continuation as a regularization work at all?

The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
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### $d=2$ pole argument of quadratic divergences in Peskin & Schroeder's book

Q1: My question is, in the context of dimensional regularisation(DREG, in dimension $d$), why do they mention the absence of $d=2$ pole in the gauge theory cases[1], whereas the $d=2$ pole is not ...
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### How does the renormalization scale $\mu$ cancel in all finite observables?

In dimensional regularization, we must shift the dimensionless coupling $g$ by the renormalization scale $\mu$ (which has unit mass dimension): g \rightarrow \mu^{4-d} g \tag{1} \end{...
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### How to handle the infrared divergence of massless $\phi^4$ in scattering

For massless $\phi^4$ theory, if exterior momentums are going to zero, then this diagram will be $$\int \frac{dk^4}{k^4}$$ will suffer from infrared divergence. Because the infrared divergence, ...
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### Why do people rule out zeta regularization for renormalization?

Using zeta regularization one can get a formula for regularizing the integral $\int_{a}^{\infty}x^{m-s}\text dx$ for any $m$. However, I have not seen anywhere. For example, I do not know why in ...
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### Cutoff regularization: Why not cutoff exactly at the momentum reached in an experiment?

So far I have only actually calculated dimensional regularization and I just know about the idea of cutoff regularization. From what I understand, as the name suggests, you just ignore momentum as ...
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### can we PHYSCALLY (not by mathematics) justify that $\zeta (-s)= 1+2^{s}+3^{s}+4^{s}+…$

the values $\zeta (-1)= -1/12$ and $\zeta (-3)= 1/120$ give accurate results for casimir and to evaluate the dimension in bosonic string theory so is there a physcial JUSTIFICATION to justify ...
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Under the ordinary Pauli -Villars Regularisation one introduces a heavy mass ($\Lambda$) term $$\frac{1}{p^2-m^2+i\epsilon} \rightarrow \frac{1}{p^2-m^2+i\epsilon} - \frac{1}{p^2-\Lambda^2+i\epsilon}.... 0answers 73 views ### Signs of Grandi's series 1-1+1-1+1-1+1+\ldots in the real world? I'm talking about the convergence of the series 1-1+1-1+1-1+1+\ldots to 1/2. I was discussing with some friends (we study physics) and I argued that Cesaro summation is a fair extension of the ... 0answers 54 views ### Dependence of finite part of loop integral on regularization Recently I've calculated some process in which arise triangle loop with running two W bosons and one massless fermion. The expression for integral is following:$$ I_{\alpha \beta}(r, q) = \int \...
We know that, in four dimensions, shifting the integration variables is valid only for convergent and logarithmically divergent integrals. If we employ a hard cutoff $\Lambda$, is it permissible to ...